On a two-term recurrence for the determinant of a general matrix
On a two-term recurrence for the determinant of a general matrix
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DOI：
10.1016/j.amc.2006.08.156
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发表时间：
2007-04
期刊：
影响因子：
--
通讯作者：
T. Sogabe
中科院分区：
文献类型：
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作者：
T. Sogabe
最近，El-Mikkawy [M. El-Mikkawy，关于三对角矩阵三项递归的一个注记，应用数学计算。139（2003）503-511]。Salkuyeh [D.K.张文龙，“三对角矩阵的一个三项递推式”，应用数学与计算。176（2006）442-444]。在本文中，我们证明了对于一般矩阵，这种关系也可以得到，并且作为副产品，我们得到了DETGTRI算法的推广[M. El-Mikkawy，一种计算n阶三对角行列式的快速算法，J. Comput. 166（2004）581-584]。
Recently, a two-term recurrence for computing the determinant of a tridiagonal matrix has been found by El-Mikkawy [M. El-Mikkawy, A note on a three-term recurrence for a tridiagonal matrix, Appl. Math. Comput. 139 (2003) 503–511]. Then, the result has been extended to a block-tridiagonal matrix by Salkuyeh [D.K. Salkuyeh, Comments on “A note on a three-term recurrence for a tridiagonal matrix”, Appl. Math. Comput. 176 (2006) 442–444]. In this note, we show that the relation can be obtained for a general matrix and that as a by-product we obtain a generalization of the DETGTRI algorithm [M. El-Mikkawy, A fast algorithm for evaluating nth order tri-diagonal determinants, J. Comput. Appl. Math. 166 (2004) 581–584].